7.3 - Proving Triangles Similar

7.3 - Proving Triangles Similar

By Steve Dull

Objective

To prove triangles similar by AA~, SSS~, or SAS~

Flashback to Triangle Congruence:

Recall AAA could not be used to prove two triangles congruent

But we now know that if corresponding angles are congruent and lengths of corresponding side are in proportion then two triangles are similar.

​

Is there a rule for proving triangles similar with less than all six pieces of information?​

Turns out there are three

• ​Angle Angle Similarity (AA~)

• Side Side Side Similarity (SSS~)

• Side Angle Side​ Similarity (SAS~)

Angle Angle Similarity

If two corresponding angles are congruent, then the triangles are similar.

Open Ended

Write a similarity statement for the triangles.

If all corresponding sides are proportional, then the triangles are similar.

Side Side Side Similarity

Some text here about the topic of discussion

Multiple Choice

Write the extended ratio to prove the triangles are similar.

• $$\frac{3}{6}=\frac{5}{8}=\frac{10}{4}$$  

• $$1:2$$  

• $$\frac{6}{3}=\frac{8}{4}=\frac{10}{5}$$  

• The triangles are not similar.

Side Angle Side Similarity

If two corresponding sides are proportional and the included angles are congruent, then the triangles are similar.

Open Ended

Write a similarity statement for the two triangles.

Multiple Choice

What postulate could you use to prove the triangles similar?

• AA Similarity

• SSS Similarity

• SAS Similarity

• The triangles are not similar.

Now try #16 on your own

​Are the triangles similar? Show your work and write a similarity statement.